--- /dev/null
+LIST
+Makefile
+asin.c
+atan.c
+atan2.c
+ceil.c
+exp.c
+fabs.c
+floor.c
+fmod.c
+frexp.e
+ldexp.c
+localmath.h
+log.c
+log10.c
+modf.e
+pow.c
+sin.c
+sinh.c
+sqrt.c
+tan.c
+tanh.c
-mlib
localmath.h
asin.c
atan2.c
atan.c
ceil.c
-cosh.c
fabs.c
pow.c
log10.c
sin.c
sinh.c
sqrt.c
-ldexp.c
tan.c
tanh.c
exp.c
+ldexp.c
+fmod.c
floor.c
+frexp.e
+modf.e
--- /dev/null
+CFLAGS=-L -LIB
+
+.SUFFIXES: .o .e .c
+
+.e.o:
+ $(CC) $(CFLAGS) -c -o $@ $*.e
+
+clean:
+ rm -rf asin.o atan2.o atan.o ceil.o fabs.o pow.o log10.o \
+ log.o sin.o sinh.o sqrt.o tan.o tanh.o exp.o ldexp.o \
+ fmod.o floor.o frexp.o modf.o OLIST
+
+asin.o:
+atan2.o:
+atan.o:
+ceil.o:
+fabs.o:
+pow.o:
+log10.o:
+log.o:
+sin.o:
+sinh.o:
+sqrt.o:
+tan.o:
+tanh.o:
+exp.o:
+ldexp.o:
+fmod.o:
+floor.o:
+frexp.o:
+modf.o:
*/
/* $Header$ */
-#include <errno.h>
#include <math.h>
+#include <errno.h>
#include "localmath.h"
-
static double
asin_acos(double x, int cosfl)
{
int negative = x < 0;
+ int i;
+ double g;
+ static double p[] = {
+ -0.27368494524164255994e+2,
+ 0.57208227877891731407e+2,
+ -0.39688862997540877339e+2,
+ 0.10152522233806463645e+2,
+ -0.69674573447350646411e+0
+ };
+ static double q[] = {
+ -0.16421096714498560795e+3,
+ 0.41714430248260412556e+3,
+ -0.38186303361750149284e+3,
+ 0.15095270841030604719e+3,
+ -0.23823859153670238830e+2,
+ 1.0
+ };
if (negative) {
x = -x;
}
- if (x > 1) {
- errno = EDOM;
- return 0;
+ if (x > 0.5) {
+ i = 1;
+ if (x > 1) {
+ errno = EDOM;
+ return 0;
+ }
+ g = 0.5 - 0.5 * x;
+ x = - sqrt(g);
+ x += x;
}
- if (x == 1) {
- x = M_PI_2;
+ else {
+ /* ??? avoid underflow ??? */
+ i = 0;
+ g = x * x;
}
- else x = atan(x/sqrt(1-x*x));
- if (negative) x = -x;
+ x += x * g * POLYNOM4(g, p) / POLYNOM5(g, q);
if (cosfl) {
- return M_PI_2 - x;
+ if (! negative) x = -x;
+ }
+ if ((cosfl == 0) == (i == 1)) {
+ x = (x + M_PI_4) + M_PI_4;
+ }
+ else if (cosfl && negative && i == 1) {
+ x = (x + M_PI_2) + M_PI_2;
}
+ if (! cosfl && negative) x = -x;
return x;
}
*/
/* $Header$ */
-#include <errno.h>
#include <float.h>
#include <math.h>
#include "localmath.h"
double
atan(double x)
{
- /* The interval [0, infinity) is treated as follows:
- Define partition points Xi
- X0 = 0
- X1 = tan(pi/16)
- X2 = tan(3pi/16)
- X3 = tan(5pi/16)
- X4 = tan(7pi/16)
- X5 = infinity
- and evaluation nodes xi
- x2 = tan(2pi/16)
- x3 = tan(4pi/16)
- x4 = tan(6pi/16)
- x5 = infinity
- An argument x in [Xn-1, Xn] is now reduced to an argument
- t in [-X1, X1] by the following formulas:
-
- t = 1/xn - (1/(xn*xn) + 1)/((1/xn) + x)
-
- arctan(x) = arctan(xi) + arctan(t)
-
- For the interval [0, p/16] an approximation is used:
- arctan(x) = x * P(x*x)/Q(x*x)
+ /* Algorithm and coefficients from:
+ "Software manual for the elementary functions"
+ by W.J. Cody and W. Waite, Prentice-Hall, 1980
*/
- static struct precomputed {
- double X; /* partition point */
- double arctan; /* arctan of evaluation node */
- double one_o_x; /* 1 / xn */
- double one_o_xsq_p_1; /* 1 / (xn*xn) + 1 */
- } prec[5] = {
- { 0.19891236737965800691159762264467622,
- 0.0,
- 0.0, /* these don't matter */
- 0.0 } ,
- { 0.66817863791929891999775768652308076, /* tan(3pi/16) */
- M_PI_8,
- 2.41421356237309504880168872420969808,
- 6.82842712474619009760337744841939616 },
- { 1.49660576266548901760113513494247691, /* tan(5pi/16) */
- M_PI_4,
- 1.0,
- 2.0 },
- { 5.02733949212584810451497507106407238, /* tan(7pi/16) */
- M_3PI_8,
- 0.41421356237309504880168872420969808,
- 1.17157287525380998659662255158060384 },
- { DBL_MAX,
- M_PI_2,
- 0.0,
- 1.0 }};
- /* Hart & Cheney # 5037 */
-
- static double p[5] = {
- 0.7698297257888171026986294745e+03,
- 0.1557282793158363491416585283e+04,
- 0.1033384651675161628243434662e+04,
- 0.2485841954911840502660889866e+03,
- 0.1566564964979791769948970100e+02
+ static double p[] = {
+ -0.13688768894191926929e+2,
+ -0.20505855195861651981e+2,
+ -0.84946240351320683534e+1,
+ -0.83758299368150059274e+0
};
-
- static double q[6] = {
- 0.7698297257888171026986294911e+03,
- 0.1813892701754635858982709369e+04,
- 0.1484049607102276827437401170e+04,
- 0.4904645326203706217748848797e+03,
- 0.5593479839280348664778328000e+02,
- 0.1000000000000000000000000000e+01
+ static double q[] = {
+ 0.41066306682575781263e+2,
+ 0.86157349597130242515e+2,
+ 0.59578436142597344465e+2,
+ 0.15024001160028576121e+2,
+ 1.0
+ };
+ static double a[] = {
+ 0.0,
+ 0.52359877559829887307710723554658381, /* pi/6 */
+ M_PI_2,
+ 1.04719755119659774615421446109316763 /* pi/3 */
};
- int negative = x < 0.0;
- register struct precomputed *pr = prec;
+ int neg = x < 0;
+ int n;
+ double g;
- if (negative) {
+ if (neg) {
x = -x;
}
- while (x > pr->X) pr++;
- if (pr != prec) {
- x = pr->arctan +
- atan(pr->one_o_x - pr->one_o_xsq_p_1/(pr->one_o_x + x));
+ if (x > 1.0) {
+ x = 1.0/x;
+ n = 2;
}
- else {
- double xsq = x*x;
+ else n = 0;
- x = x * POLYNOM4(xsq, p)/POLYNOM5(xsq, q);
+ if (x > 0.26794919243112270647) { /* 2-sqtr(3) */
+ n = n + 1;
+ x = (((0.73205080756887729353*x-0.5)-0.5)+x)/
+ (1.73205080756887729353+x);
}
- return negative ? -x : x;
-}
+ /* ??? avoid underflow ??? */
+
+ g = x * x;
+ x += x * g * POLYNOM3(g, p) / POLYNOM4(g, q);
+ if (n > 1) x = -x;
+ x += a[n];
+ return neg ? -x : x;
+}
*/
/* $Header$ */
-#include <errno.h>
#include <math.h>
+#include <errno.h>
#include "localmath.h"
double
*/
/* $Header$ */
-#include <errno.h>
-#include <float.h>
#include <math.h>
+#include <float.h>
+#include <errno.h>
#include "localmath.h"
double
exp(double x)
{
- /* 2**x = (Q(x*x)+x*P(x*x))/(Q(x*x)-x*P(x*x)) for x in [0,0.5] */
- /* Hart & Cheney #1069 */
+ /* Algorithm and coefficients from:
+ "Software manual for the elementary functions"
+ by W.J. Cody and W. Waite, Prentice-Hall, 1980
+ */
- static double p[3] = {
- 0.2080384346694663001443843411e+07,
- 0.3028697169744036299076048876e+05,
- 0.6061485330061080841615584556e+02
+ static double p[] = {
+ 0.25000000000000000000e+0,
+ 0.75753180159422776666e-2,
+ 0.31555192765684646356e-4
};
- static double q[4] = {
- 0.6002720360238832528230907598e+07,
- 0.3277251518082914423057964422e+06,
- 0.1749287689093076403844945335e+04,
- 0.1000000000000000000000000000e+01
+ static double q[] = {
+ 0.50000000000000000000e+0,
+ 0.56817302698551221787e-1,
+ 0.63121894374398503557e-3,
+ 0.75104028399870046114e-6
};
-
- int negative = x < 0;
- int ipart, large = 0;
- double xsqr, xPxx, Qxx;
+ double xn, g;
+ int n;
+ int negative = x < 0;
if (x <= M_LN_MIN_D) {
if (x < M_LN_MIN_D) errno = ERANGE;
return DBL_MAX;
}
- if (negative) {
- x = -x;
+ if (negative) x = -x;
+
+ /* ??? avoid underflow ??? */
+
+ n = x * M_LOG2E + 0.5; /* 1/ln(2) = log2(e), 0.5 added for rounding */
+ xn = n;
+ {
+ double x1 = (long) x;
+ double x2 = x - x1;
+
+ g = ((x1-xn*0.693359375)+x2) - xn*(-2.1219444005469058277e-4);
}
- x /= M_LN2;
- ipart = floor(x);
- x -= ipart;
- if (x > 0.5) {
- large = 1;
- x -= 0.5;
+ if (negative) {
+ g = -g;
+ n = -n;
}
- xsqr = x * x;
- xPxx = x * POLYNOM2(xsqr, p);
- Qxx = POLYNOM3(xsqr, q);
- x = (Qxx + xPxx) / (Qxx - xPxx);
- if (large) x *= M_SQRT2;
- x = ldexp(x, ipart);
- if (negative) return 1.0/x;
- return x;
+ xn = g * g;
+ x = g * POLYNOM2(xn, p);
+ n += 1;
+ return (ldexp(0.5 + x/(POLYNOM3(xn, q) - x), n));
}
--- /dev/null
+/*
+ * (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
+ * See the copyright notice in the ACK home directory, in the file "Copyright".
+ *
+ * Author: Hans van Eck
+ */
+/* $Header$ */
+
+#include <math.h>
+#include <errno.h>
+
+double
+fmod(double x, double y)
+{
+ long i;
+ double val;
+ double frac;
+
+ if (y == 0) {
+ errno = EDOM;
+ return 0;
+ }
+ frac = modf( x / y, &val);
+
+ return frac * y;
+
+/*
+ val = x / y;
+ if (val > LONG_MIN && val < LONG_MAX) {
+ i = val;
+ return x - i * y;
+ }
+*/
+}
*/
/* $Header$ */
- mes 2,EM_WSIZE,EM_PSIZE
+ mes 2,_EM_WSIZE,_EM_PSIZE
#ifndef NOFLOAT
exp $frexp
pro $frexp,0
lal 0
- loi EM_DSIZE
- fef EM_DSIZE
- lal EM_DSIZE
- loi EM_PSIZE
- sti EM_WSIZE
- ret EM_DSIZE
+ loi _EM_DSIZE
+ fef _EM_DSIZE
+ lal _EM_DSIZE
+ loi _EM_PSIZE
+ sti _EM_WSIZE
+ ret _EM_DSIZE
end
#endif
#define POLYNOM13(x, a) (POLYNOM12((x),(a)+1)*(x)+(a)[0])
#define M_LN_MAX_D (M_LN2 * DBL_MAX_EXP)
-#define M_LN_MIN_D (M_LN2 * (DBL_MAX_EXP - 1))
+#define M_LN_MIN_D (M_LN2 * (DBL_MIN_EXP - 1))
*/
/* $Header$ */
-#include <errno.h>
#include <math.h>
+#include <errno.h>
#include "localmath.h"
-
double
log(double x)
{
- /* log(x) = z*P(z*z)/Q(z*z), z = (x-1)/(x+1), x in [1/sqrt(2), sqrt(2)]
+ /* Algorithm and coefficients from:
+ "Software manual for the elementary functions"
+ by W.J. Cody and W. Waite, Prentice-Hall, 1980
*/
- /* Hart & Cheney #2707 */
-
- static double p[5] = {
- 0.7504094990777122217455611007e+02,
- -0.1345669115050430235318253537e+03,
- 0.7413719213248602512779336470e+02,
- -0.1277249755012330819984385000e+02,
- 0.3327108381087686938144000000e+00
+ static double a[] = {
+ -0.64124943423745581147e2,
+ 0.16383943563021534222e2,
+ -0.78956112887491257267e0
};
-
- static double q[5] = {
- 0.3752047495388561108727775374e+02,
- -0.7979028073715004879439951583e+02,
- 0.5616126132118257292058560360e+02,
- -0.1450868091858082685362325000e+02,
- 0.1000000000000000000000000000e+01
+ static double b[] = {
+ -0.76949932108494879777e3,
+ 0.31203222091924532844e3,
+ -0.35667977739034646171e2,
+ 1.0
};
- double z, zsqr;
- int exponent;
+ double znum, zden, z, w;
+ int exponent;
- if (x <= 0) {
+ if (x < 0) {
errno = EDOM;
- return 0;
+ return -HUGE_VAL;
+ }
+ else if (x == 0) {
+ errno = ERANGE;
+ return -HUGE_VAL;
}
x = frexp(x, &exponent);
- while (x < M_1_SQRT2) {
- x += x;
+ if (x > M_1_SQRT2) {
+ znum = (x - 0.5) - 0.5;
+ zden = x * 0.5 + 0.5;
+ }
+ else {
+ znum = x - 0.5;
+ zden = znum * 0.5 + 0.5;
exponent--;
}
- z = (x-1)/(x+1);
- zsqr = z*z;
- return z * POLYNOM4(zsqr, p) / POLYNOM4(zsqr, q) + exponent * M_LN2;
+ z = znum/zden; w = z * z;
+ x = z + z * w * (POLYNOM2(w,a)/POLYNOM3(w,b));
+ z = exponent;
+ x += z * (-2.121944400546905827679e-4);
+ return x + z * 0.693359375;
}
*/
/* $Header$ */
-#include <errno.h>
#include <math.h>
+#include <errno.h>
#include "localmath.h"
double
log10(double x)
{
- if (x <= 0) {
+ if (x < 0) {
errno = EDOM;
- return 0;
+ return -HUGE_VAL;
+ }
+ else if (x == 0) {
+ errno = ERANGE;
+ return -HUGE_VAL;
}
return log(x) / M_LN10;
*/
/* $Header$ */
- mes 2,EM_WSIZE,EM_PSIZE
+ mes 2,_EM_WSIZE,_EM_PSIZE
#ifndef NOFLOAT
exp $modf
pro $modf,0
lal 0
- loi EM_DSIZE
+ loi _EM_DSIZE
loc 1
- loc EM_WSIZE
- loc EM_DSIZE
+ loc _EM_WSIZE
+ loc _EM_DSIZE
cif
- fif EM_DSIZE
- lal EM_DSIZE
- loi EM_PSIZE
- sti EM_DSIZE
- ret EM_DSIZE
+ fif _EM_DSIZE
+ lal _EM_DSIZE
+ loi _EM_PSIZE
+ sti _EM_DSIZE
+ ret _EM_DSIZE
end
#endif
*/
/* $Header$ */
-#include <errno.h>
#include <math.h>
+#include <float.h>
+#include <errno.h>
+#include "localmath.h"
double
pow(double x, double y)
{
+ /* Simple version for now. The Cody and Waite book has
+ a very complicated, much more precise version, but
+ this version has machine-dependent arrays A1 and A2,
+ and I don't know yet how to solve this ???
+ */
double dummy;
+ int result_neg = 0;
if ((x == 0 && y == 0) ||
(x < 0 && modf(y, &dummy) != 0)) {
if (x == 0) return x;
if (x < 0) {
- double val = exp(log(-x) * y);
if (modf(y/2.0, &dummy) != 0) {
/* y was odd */
- val = - val;
+ result_neg = 1;
}
- return val;
+ x = -x;
+ }
+ x = log(x);
+ if (x < 0) {
+ x = -x;
+ y = -y;
+ }
+ if (y > M_LN_MAX_D/x) {
+ errno = ERANGE;
+ return 0;
+ }
+ if (y < M_LN_MIN_D/x) {
+ errno = ERANGE;
+ return 0;
}
- return exp(log(x) * y);
+ x = exp(x * y);
+ return result_neg ? -x : x;
}
*/
/* $Header$ */
-#include <errno.h>
#include <math.h>
#include "localmath.h"
static double
-sinus(double x, int quadrant)
+sinus(double x, int cos_flag)
{
- /* sin(0.5*pi*x) = x * P(x*x)/Q(x*x) for x in [0,1] */
- /* Hart & Cheney # 3374 */
+ /* Algorithm and coefficients from:
+ "Software manual for the elementary functions"
+ by W.J. Cody and W. Waite, Prentice-Hall, 1980
+ */
- static double p[6] = {
- 0.4857791909822798473837058825e+10,
- -0.1808816670894030772075877725e+10,
- 0.1724314784722489597789244188e+09,
- -0.6351331748520454245913645971e+07,
- 0.1002087631419532326179108883e+06,
- -0.5830988897678192576148973679e+03
+ static double r[] = {
+ -0.16666666666666665052e+0,
+ 0.83333333333331650314e-2,
+ -0.19841269841201840457e-3,
+ 0.27557319210152756119e-5,
+ -0.25052106798274584544e-7,
+ 0.16058936490371589114e-9,
+ -0.76429178068910467734e-12,
+ 0.27204790957888846175e-14
};
- static double q[6] = {
- 0.3092566379840468199410228418e+10,
- 0.1202384907680254190870913060e+09,
- 0.2321427631602460953669856368e+07,
- 0.2848331644063908832127222835e+05,
- 0.2287602116741682420054505174e+03,
- 0.1000000000000000000000000000e+01
- };
-
- double xsqr;
- int t;
+ double xsqr;
+ double y;
+ int neg = 0;
if (x < 0) {
- quadrant += 2;
x = -x;
+ neg = 1;
}
- if (M_PI_2 - x == M_PI_2) {
- switch(quadrant) {
- case 0:
- case 2:
- return 0.0;
- case 1:
- return 1.0;
- case 3:
- return -1.0;
- }
+ if (cos_flag) {
+ neg = 0;
+ y = M_PI_2 + x;
}
- if (x >= M_2PI) {
- if (x <= 0x7fffffff) {
- /* Use extended precision to calculate reduced argument.
- Split 2pi in 2 parts a1 and a2, of which the first only
- uses some bits of the mantissa, so that n * a1 is
- exactly representable, where n is the integer part of
- x/pi.
- Here we used 12 bits of the mantissa for a1.
- Also split x in integer part x1 and fraction part x2.
- We then compute x-n*2pi as ((x1 - n*a1) + x2) - n*a2.
- */
-#define A1 6.2822265625
-#define A2 0.00095874467958647692528676655900576
- double n = (long) (x / M_2PI);
- double x1 = (long) x;
- double x2 = x - x1;
- x = x1 - n * A1;
+ else y = x;
+
+ /* ??? avoid loss of significance, if y is too large, error ??? */
+
+ y = y * M_1_PI + 0.5;
+
+ /* Use extended precision to calculate reduced argument.
+ Here we used 12 bits of the mantissa for a1.
+ Also split x in integer part x1 and fraction part x2.
+ */
+#define A1 3.1416015625
+#define A2 -8.908910206761537356617e-6
+ {
+ double x1, x2;
+
+ modf(y, &y);
+ if (modf(0.5*y, &x1)) neg = !neg;
+ if (cos_flag) y -= 0.5;
+ x2 = modf(x, &x1);
+ x = x1 - y * A1;
x += x2;
- x -= n * A2;
+ x -= y * A2;
#undef A1
#undef A2
- }
- else {
- double dummy;
-
- x = modf(x/M_2PI, &dummy) * M_2PI;
- }
- }
- x /= M_PI_2;
- t = x;
- x -= t;
- quadrant = (quadrant + (int)(t % 4)) % 4;
- if (quadrant & 01) {
- x = 1 - x;
}
- if (quadrant > 1) {
+
+ if (x < 0) {
+ neg = !neg;
x = -x;
}
- xsqr = x * x;
- x = x * POLYNOM5(xsqr, p) / POLYNOM5(xsqr, q);
- return x;
+
+ /* ??? avoid underflow ??? */
+
+ y = x * x;
+ x += x * y * POLYNOM7(y, r);
+ return neg ? -x : x;
}
double
*/
/* $Header$ */
-#include <errno.h>
#include <math.h>
+#include <float.h>
+#include <errno.h>
#include "localmath.h"
-double
-sinh(double x)
+static double
+sinh_cosh(double x, int cosh_flag)
{
- int negx = x < 0;
+ /* Algorithm and coefficients from:
+ "Software manual for the elementary functions"
+ by W.J. Cody and W. Waite, Prentice-Hall, 1980
+ */
+
+ static double p[] = {
+ -0.35181283430177117881e+6,
+ -0.11563521196851768270e+5,
+ -0.16375798202630751372e+3,
+ -0.78966127417357099479e+0
+ };
+ static double q[] = {
+ -0.21108770058106271242e+7,
+ 0.36162723109421836460e+5,
+ -0.27773523119650701167e+3,
+ 1.0
+ };
+ int negative = x < 0;
+ double y = negative ? -x : x;
- if (negx) {
- x = -x;
+ if (! cosh_flag && y <= 1.0) {
+ /* ??? check for underflow ??? */
+ y = y * y;
+ return x + x * y * POLYNOM3(y, p)/POLYNOM3(y,q);
}
- if (x > M_LN_MAX_D) {
- /* exp(x) would overflow */
- if (x >= M_LN_MAX_D + M_LN2) {
- /* not representable */
- x = HUGE_VAL;
+
+ if (y >= M_LN_MAX_D) {
+ /* exp(y) would cause overflow */
+#define LNV 0.69316101074218750000e+0
+#define VD2M1 0.52820835025874852469e-4
+ double w = y - LNV;
+
+ if (w < M_LN_MAX_D+M_LN2-LNV) {
+ x = exp(w);
+ x += VD2M1 * x;
+ }
+ else {
errno = ERANGE;
+ x = HUGE_VAL;
}
- else x = exp (x - M_LN2);
}
else {
- double expx = exp(x);
- x = 0.5 * (expx - 1.0/expx);
- }
- if (negx) {
- return -x;
+ double z = exp(y);
+
+ x = 0.5 * (z + (cosh_flag ? 1.0 : -1.0)/z);
}
- return x;
+ return negative ? -x : x;
+}
+
+double
+sinh(double x)
+{
+ return sinh_cosh(x, 0);
+}
+
+double
+cosh(double x)
+{
+ if (x < 0) x = -x;
+ return sinh_cosh(x, 1);
}
*/
/* $Header$ */
-#include <errno.h>
#include <math.h>
+#include <errno.h>
#define NITER 5
*/
/* $Header$ */
-#include <errno.h>
#include <math.h>
#include "localmath.h"
-
double
tan(double x)
{
- /* First reduce range to [0, pi/4].
- Then use approximation tan(x*pi/4) = x * P(x*x)/Q(x*x).
- Hart & Cheney # 4288
- Use: tan(x) = 1/tan(pi/2 - x)
- tan(-x) = -tan(x)
- tan(x+k*pi) = tan(x)
+ /* Algorithm and coefficients from:
+ "Software manual for the elementary functions"
+ by W.J. Cody and W. Waite, Prentice-Hall, 1980
*/
- static double p[5] = {
- -0.5712939549476836914932149599e+10,
- 0.4946855977542506692946040594e+09,
- -0.9429037070546336747758930844e+07,
- 0.5282725819868891894772108334e+05,
- -0.6983913274721550913090621370e+02
- };
-
- static double q[6] = {
- -0.7273940551075393257142652672e+10,
- 0.2125497341858248436051062591e+10,
- -0.8000791217568674135274814656e+08,
- 0.8232855955751828560307269007e+06,
- -0.2396576810261093558391373322e+04,
- 0.1000000000000000000000000000e+01
- };
-
int negative = x < 0;
- double tmp, tmp1, tmp2;
- double xsq;
int invert = 0;
- int ip;
+ double y;
+ static double p[] = {
+ 1.0,
+ -0.13338350006421960681e+0,
+ 0.34248878235890589960e-2,
+ -0.17861707342254426711e-4
+ };
+ static double q[] = {
+ 1.0,
+ -0.46671683339755294240e+0,
+ 0.25663832289440112864e-1,
+ -0.31181531907010027307e-3,
+ 0.49819433993786512270e-6
+ };
if (negative) x = -x;
+
+ /* ??? avoid loss of significance, error if x is too large ??? */
- /* first reduce to [0, pi) */
- if (x >= M_PI) {
- if (x <= 0x7fffffff) {
- /* Use extended precision to calculate reduced argument.
- Split pi in 2 parts a1 and a2, of which the first only
- uses some bits of the mantissa, so that n * a1 is
- exactly representable, where n is the integer part of
- x/pi.
- Here we used 12 bits of the mantissa for a1.
- Also split x in integer part x1 and fraction part x2.
- We then compute x-n*pi as ((x1 - n*a1) + x2) - n*a2.
- */
-#define A1 3.14111328125
-#define A2 0.00047937233979323846264338327950288
- double n = (long) (x / M_PI);
- double x1 = (long) x;
- double x2 = x - x1;
- x = x1 - n * A1;
- x += x2;
- x -= n * A2;
-#undef A1
-#undef A2
- }
- else {
- x = modf(x/M_PI, &tmp) * M_PI;
- }
- }
- /* because the approximation uses x*pi/4, we reverse this */
- x /= M_PI_4;
- ip = (int) x;
- x -= ip;
+ y = x * M_2_PI + 0.5;
- switch(ip) {
- case 0:
- /* [0,pi/4] */
- break;
- case 1:
- /* [pi/4, pi/2]
- tan(x+pi/4) = 1/tan(pi/2 - (x+pi/4)) = 1/tan(pi/4 - x)
- */
- invert = 1;
- x = 1.0 - x;
- break;
- case 2:
- /* [pi/2, 3pi/4]
- tan(x+pi/2) = tan((x+pi/2)-pi) = -tan(pi/2 - x) =
- -1/tan(x)
- */
- negative = ! negative;
- invert = 1;
- break;
- case 3:
- /* [3pi/4, pi)
- tan(x+3pi/4) = tan(x-pi/4) = - tan(pi/4-x)
- */
- x = 1.0 - x;
- negative = ! negative;
- break;
- }
- xsq = x * x;
- tmp1 = x*POLYNOM4(xsq, p);
- tmp2 = POLYNOM5(xsq, q);
- tmp = tmp1 / tmp2;
- if (invert) {
- if (tmp == 0.0) {
- errno = ERANGE;
- tmp = HUGE_VAL;
- }
- else tmp = tmp2 / tmp1;
+ /* Use extended precision to calculate reduced argument.
+ Here we used 12 bits of the mantissa for a1.
+ Also split x in integer part x1 and fraction part x2.
+ */
+ #define A1 1.57080078125
+ #define A2 -4.454455103380768678308e-6
+ {
+ double x1, x2;
+
+ modf(y, &y);
+ if (modf(0.5*y, &x1)) invert = 1;
+ x2 = modf(x, &x1);
+ x = x1 - y * A1;
+ x += x2;
+ x -= y * A2;
+ #undef A1
+ #undef A2
}
- return negative ? -tmp : tmp;
+ /* ??? avoid underflow ??? */
+ y = x * x;
+ x += x * y * POLYNOM2(y, p+1);
+ y = POLYNOM4(y, q);
+ if (negative) x = -x;
+ return invert ? -y/x : x/y;
}
*/
/* $Header$ */
-#include <errno.h>
+#include <float.h>
#include <math.h>
#include "localmath.h"
double
tanh(double x)
{
- if (x <= 0.5*M_LN_MIN_D) {
- return -1;
- }
+ /* Algorithm and coefficients from:
+ "Software manual for the elementary functions"
+ by W.J. Cody and W. Waite, Prentice-Hall, 1980
+ */
+
+ static double p[] = {
+ -0.16134119023996228053e+4,
+ -0.99225929672236083313e+2,
+ -0.96437492777225469787e+0
+ };
+ static double q[] = {
+ 0.48402357071988688686e+4,
+ 0.22337720718962312926e+4,
+ 0.11274474380534949335e+3,
+ 1.0
+ };
+ int negative = x < 0;
+
+ if (negative) x = -x;
+
if (x >= 0.5*M_LN_MAX_D) {
- return 1;
+ x = 1.0;
+ }
+#define LN3D2 0.54930614433405484570e+0 /* ln(3)/2 */
+ else if (x > LN3D2) {
+ x = 0.5 - 1.0/(exp(x+x)+1.0);
+ x += x;
+ }
+ else {
+ /* ??? avoid underflow ??? */
+ double g = x*x;
+ x += x * g * POLYNOM2(g, p)/POLYNOM3(g, q);
}
- x = exp(x + x);
- return (x - 1.0)/(x + 1.0);
+ return negative ? -x : x;
}
public / ack.git / commitdiff